Abstract
This paper presents three definitions of equivalent stress calculation for micropolar solids. After a short review of the literature, the kinematical, equlibrium and constitutive equations are summarized. Applying the definition of the elastic strain energy, the paper gives three methods for the determination of equivalent stresses. After that, these are compared by a known cyilinder torsion analitical example from literature.
Highlights
Conventional formulation of continuum mechanics approaches cannot incorporate any intrinsic material length scales
Real materials often exhibit a number of important length scales, which must be included in any realistic model: foams, granular materials, ceramics, biological tissues, fibers, particles, cellular solids and composites
This paper presents three different models for definitions of equivalent stress, which contain the material parameters [7], so these can be using in numerical examples
Summary
Conventional formulation of continuum mechanics approaches cannot incorporate any intrinsic material length scales. Forest [5] defined a general formula, but the constants what were used in the equations, are not identified by material parameters. This paper presents three different models for definitions of equivalent stress, which contain the material parameters [7], so these can be using in numerical examples. All three definitions are based on the relation of general and uniaxial stress state, but these neglect different parts of the elastic strain energy.
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